Find the arclength L(C) of the helix C parametrized by C: r(t) = (2 cos t, -3t, 2 sin t) for 0

Q: Find r'(t) r(t) = 6Vti + t²V¢j + In(2 )k r'(t) =

A: Given r(t)=6ti+t2tj+ln(t2)kThat is…

Q: 5. Find the general solution: 9y" + 12y' + 4y = 0.

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Q: test conerg ence and clivergence h!

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Q: An archaeologist found a burial jar when excavating in an ancient village. To determine the age of…

A: Rate of decay of C14 is proportional to its amountdctdt=kct…

Q: 1. Solve for x, if 0 < 0 < 2n. Write your answers in exact values only. 2 2cos" x + cos x- 1 0

A: Given: 2cos2x+cosx-1=0  and 0≤θ≤2πlet cosx=mthen 2cos2x+cosx-1=0        2m2+m-1=0We know that root…

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 5 cos(t)i…

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x + 3 lim x--3 x + 27

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Q: 2-2 +2)Xx+1) (*+1P Option 1 Option 2 1. (x +1) *+2 (x +1) Option 3 Option 4

A: This question is related to partial fraction decomposition, we will solve it using given…

Q: xe - ye" = In(xy). Find dy/dx.

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Q: test conerg ence and divergence h!

A: We can solve this as follows:

Q: Question 4 Given the following equation, determine y'using the methods discussed in class a - y3 =…

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Q: The marginal cost for a company to produce q items is given by MC(q) = 0.002q -0.7q +620. The…

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Q: Evaluate the following indefinite integral: x dx 1.) S- Vx4 - 1

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Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) = -…

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Q: Evaluate (2x - y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (5, -5)

A: The objective of the question is evaluate the definite integral.

Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

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Q: Evaluate: 3 A 1–x*) 2 + C 3 (1-x*) ² + C --(1-x*) ² +C D 1-x*) 2 + C 3

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Q: Find the Maclaurin series for f(r) using the definition of a Maclaurin series. [Assume that has a…

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Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: Sezx(1 + e-2*)dx

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Q: 2. (Section 9.2) A refinery produces both gasoline and fuel oil, and sells the gasoline for $4.00…

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Q: y' + 4y = e^(4t) %3D

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Q: '글 +2+글 +5 The sum +8+ +11 written in sigma notation is equal to 8 3k-2 A k=1 2 8 3k - 1 B k=1 8 3k…

A: The sum 1/2 +2+7/2 +5+13/2 +8+19/2 +11.

Q: 21 3x7 + 8x 5x

A: Given: y=3x7+8x5-215x

Q: 1. Solve the differential equation: xy' – y = 2x In x

A: Use linear differential equation concept

Q: 1

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Q: 5 x X LOS

A: Given: I=∫0πsin5x2cos7x2dx  ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: d Calculate r1(t) · r2(t)] and dt d [ri(t) × r2(t)] first by differentiating the product directly…

A: Given that,       r1(t)=9t i+4t2j+5t3k,   r2(t)=t4k

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

Q: 3. Compute f(x)dx 2х if x<1 f(x) = { 4 if x21

A: As we know from the property of the definite integral. ∫abfxdx=∫acfxdx+∫cbfxdx And The Power rule:…

Q: Evaluate the integral.

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Q: Find the volume of the solid obtained by rotating about the x-axis the region under the curve y=…

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Q: 1 Which of the following is an antiderivative of the function f(r) = %3D 5+ x2 (a) 2x In(5+2?) 1 (b)…

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Q: The study of integrals in calculus is motivated by the problem of calculatin (a) the slope of a…

A: Study of integrals in calculus is motivated by calculating the area of a region bounded by curves.

Q: 6. Determine. 2r - 3x 4x SET A.

A: I have stated the used formula in the solution

Q: Find the first three non-zero terms of the Maclaurin expansion of the function. f(x) = 3 cos 2xx…

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Q: Find the moment of inertia of the area bounded by the curve x^2=8y, the line x=4 and the x-axis on…

A: Use moment of inertia concept

Q: Sx sin(3x – 2) dx |

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Q: Describe the graph of the equation. (5 – 21) i + 8tj r = It is a plane in 2-space through the point…

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Q: In 4 In 3 ex+y dxdy Evaluate I

A: According to our answering guidelines, we can answer one question at a time, therefore I am…

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: dx 2.) S 4+ x2

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Q: Describe the graph of the equation. r - 12cosri + 5sinsj -k O tis an ellipse in the z = -1 plane,…

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Q: For the given function find dy/dx. = x +2

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Q: Given f(x, y) = (3x – a²)(2y – y²). (a) Find all the critical points of the function. (b) Classify…

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Q: A spring with a natural length of 10 cm, is stretched by ½ cm by a 12 N force. Find the work done in…

A: Given query is to find the work done .

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: Determine the vector field of F. F(x, y) = 9i – 3j

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Q: Use the formula k(t) |r(t) × r"(t)|| x r" (t)|| to find «(t). ||r(t)||° r(t) = ti+ t5j «(t)

A: To find k(t).

Q: Use the properties of the derivative and the given vectors to find the following. = ti+ 8 sin(t)j +…

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